A Guardian article titled "Enlightened Princesses review – royals who shaped modern Britain" has this:

In 30 brief chapters, some only three pages long, we hear about the avant garde composers these women commissioned, the educational toys they gave their children, the libraries of new thought they assembled on their bookshelves. Some of these essays deliberately overlap – Handel pops up in a music chapter while also making an appearance in the discussion of London’s Foundling hospital, of which he was a patron. Yet far from feeling confused or excessive, this approach builds a rich allusive pattern, a sense of the cross-fertilisations that were everywhere in play. Set alongside these essays are illustrations and close readings of key objects – a useful reminder that something as airy sounding as the Enlightenment was actually grounded in the material world of a Wedgwood dinner service, an architect’s protractor, and a pocket full of solid silver coins.

The last sentence has this noun phrase a pocket full of solid silver coins. Does the phrase mean "a pocket that is full of solid silver coins" or "as many solid silver coins as a pocket can hold"?

I think it's the latter. Am I right?

If so, isn't it more correct to say "pocketful" instead of "pocket full"?

...in the material world of a Wedgwood dinner service, an architect’s protractor, and a pocketful of solid silver coins.

Or are both well-formed regardless of the exact meaning of the phrase?

A Guardian article titled "Enlightened Princesses review – royals who shaped modern Britain" has this:

In 30 brief chapters, some only three pages long, we hear about the avant garde composers these women commissioned, the educational toys they gave their children, the libraries of new thought they assembled on their bookshelves. Some of these essays deliberately overlap – Handel pops up in a music chapter while also making an appearance in the discussion of London’s Foundling hospital, of which he was a patron. Yet far from feeling confused or excessive, this approach builds a rich allusive pattern, a sense of the cross-fertilisations that were everywhere in play. Set alongside these essays are illustrations and close readings of key objects – a useful reminder that something as airy sounding as the Enlightenment was actually grounded in the material world of a Wedgwood dinner service, an architect’s protractor, and a pocket full of solid silver coins.

The last sentence has this noun phrase a pocket full of solid silver coins. Does the phrase mean "a pocket that is full of solid silver coins" or "as many solid silver coins as a pocket can hold"?

I think it's the former. Am I right?

If so, isn't it more correct to say "pocketful" instead of "pocket full"?

...in the material world of a Wedgwood dinner service, an architect’s protractor, and a pocketful of solid silver coins.

Or are both well-formed in the given context regardless of the exact meaning of the phrase?